A common situation in practical industrial applications related to product development is the need to perform many surveys inside a space of state parameters. In the specific case of aeronautics, the calculation of the pressure distribution and/or other variable distributions over an aerodynamic surface is an important feature, in order to optimally design its structural components so that the weight of the structure is the minimum possible, but at the same time being able to withstand the expected aerodynamic forces.
Thanks to the increase of the use of the Computer Fluid Simulation Capability, nowadays, the calculation of the pressure distributions and/or other variable distributions over an aerodynamic surface is commonly done by solving numerically the Reynolds Averaged Navier-Stokes equations that model the movement of the flow around the surface, using discrete finite elements, finite differences or finite volume models. With the demand of accuracy posed in the aeronautical industry, each one of these computations requires important computational resources.
As the pressure distribution and/or other variable distributions over an aerodynamic surface depend on many different flight parameters, like angle of attack and Mach number, it is necessary to perform many lengthy and costly computations to obtain all the required information.
Some methods for calculating the pressure distributions and/or other variable distributions over the surface of an aerodynamic surface such as an aircraft wing, inside a defined parameter space, using Computational Fluid Dynamics (CFD) and interpolation are known in the prior art. In particular a known interpolation method is disclosed in the article “A Multilinear Singular Value Decomposition”, Lieven De Lathauwer, Bart de Moor and Joos Vandewalle. SIAM J. Matrix Annal. Appl. Vol. 21, No. 4, pp 1253-1278.
CFD is used to calculate the pressure distributions and/or other variable distributions in a predefined group of points of the parameter space. The shock wave phenomena causes difficulties at the interpolation step. Namely, the number of computations needed to accurately reproduce the shock wave phenomena must be larger than the quantity I/d, where I stands for the geometric distance between extreme positions of the shock wave (as the parameters are varied) and d stands for the thickness of the shock wave. However, regarding that, in typical aircraft wings, the thickness of shock waves is usually small and the parameter I can be of the order of the 50% of the chord length, the number of computations needed to perform the interpolation of the shock wave increases rapidly.
The present invention is intended to solve this drawback.